Optimal convergence of a discontinuous-Galerkin-based immersed boundary method
Adrian J. Lew, Matteo Negri (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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We prove the optimal convergence of a discontinuous-Galerkin-based immersed boundary method introduced earlier [Lew and Buscaglia, (2008) 427–454]. By switching to a discontinuous Galerkin discretization near the boundary, this method overcomes the suboptimal convergence rate that may arise in immersed boundary methods when strongly imposing essential boundary conditions. We consider a model Poisson's problem with homogeneous boundary conditions over two-dimensional...